1. Field of the Invention
This invention relates a measurement technique of synthetically combining plural sets of partial measurement data obtained by means of a contact type probe and computationally determining the overall measurement data. This technique finds applications in the field of measuring a large optical element by an instrument having only a small measurable region.
2. Description of the Related Art
Partial measurement represents a technique that has been developed through shape measurement mainly using interferometers. In this specification, “a partial measurement technique” is a synonymous expression of “a stitching technique”, which is an expression that has conventionally been used. Additionally, in this specification, the expression of “the difference of the measurement data in an overlap region” means “a mismatch” that has conventionally been employed.
The partial measurement technique of this invention can be applied to and developed for coordinate measuring machines. Therefore, the difference between shape measurement by an interferometer (interferometry) and shape measurement by a coordinate measuring machine will be described first.
Interferometry is an optical measurement method of observing the interference fringe produced by a measurement wavefront that reflects the shape of a workpiece and a reference wavefront that is formed artificially by means of a camera and determining the shape from the observed interference fringe.
Generally, plural sets of measurement data show the differences from the same reference wavefront. In other words, measurement data indicates the deviations from a common offset that is the reference wavefront. Additionally, the deviations are required to be small enough to allow the interference fringe to be observed. Thus, when a measurement region is divided into a plurality of regions that overlap each other for measurement, the difference of the measurement data in an overlap region is small.
When, for example, visible light is employed, the gaps of interference fringe are of the order of sub-microns, or the differences among measurement data are of the order of microns at largest. A workpiece that requires partial measurements, or stitchings, may be a lens having a diameter of e.g. about 1 m. When compared with this size, the difference of the measurement data is very small. In short, interferometry is characterized in that the difference of partial measurement data, or the mismatch, is small in principle.
On the other hand, the measurement data of a coordinate measuring machine are a set of three-dimensional positions of points on the surface of a workpiece. In the case of a coordinate measuring machine using a contact type probe, the front end of the probe is brought into contact with the surface of the workpiece to determine the three-dimensional position of the front end of the probe. Then, the contact type probe is driven to scan the surface of the workpiece and continuously obtain data on three-dimensional positions in order to determine the profile of the surface of the workpiece.
In the measuring operation, the differences among the plurality of measurement data of the overlap regions are influenced by the position/attitude error of the machine and the fitting error of the workpiece. Generally, it is difficult to reduce the errors having six degrees of freedom because a very high degree of accuracy of installation is required.
Then, as a result, in the case of a lens having a diameter of 1 m as cited above, the differences among measurement data in the overlap regions may well exceed 1 mm. Additionally, the values of the measurement data are large if compared with those of the measurement data of interference measurement since there is not any common shape that can be subtracted from the measurement data unlike the instance of the use of a reference wavefront for interference measurement. In short, when a coordinate measuring machine is used, the differences of partial measurement data, or the mismatches, are characterized by their remarkable magnitude if compared with interference measurement.
The stitching technique of joining partial measurement data together to synthesize the entire shape is centered at the computation method of connecting measurement data. This method can be simplified to a two-step method as described below.
Step 1: Transforming plural sets of partial measurement data, using parameters
Step 2: Laying the transformed data and synthetically combining them to obtain overall measurement data
The plurality of partial measurement data can be made to overlap one on the other and synthetically combined by interpolating and averaging them in Step 2. However, since transformation methods that can be used for Step 1 are innumerable, the quality of the stitching technique depends on how an optimum transformation method is selected. Generally, parameters to be used for describing the transformation method and an evaluation function are defined and the parameters are adjusted to make the evaluation function optimum.
Currently, no optimum answer has been found yet for the technique of synthetically combining partial measurement data and hence various methods have been proposed. The differences of the proposed methods can be made clear by classifying them, paying attention to the following two points.    1 How an evaluation function and parameters are defined?    2 How the optimization problem is solved?
FIG. 12 of the accompanying drawings schematically illustrates the known technique disclosed in U.S. Pat. No. 6,956,657. This patent document proposes an evaluation function which represents “the inconsistency of data from respective data maps in the overlap regions and is expressed by linearly combining parameters”; hence the mismatch expressed by a linear combination of parameters being employed as evaluation function. Additionally, the above-cited Patent Document proposes a method of minimizing the evaluation function by making all the parameters vary simultaneously as a method of optimizing the evaluation function.
(a) and (b) of FIG. 13 of the accompanying drawings schematically illustrate another known technique disclosed in Japanese Patent No. 3182056. With the method of this patent document, a mark is arranged on a workpiece. Additionally, the patent document proposes a mismatch as an evaluation function. The above patent document also proposes a method of firstly aligning the mark and subsequently minimizing the mismatch as a method of optimizing the evaluation function.
On the other hand, a coordinate measuring machine disclosed in Japanese Patent No. 3272952 Publication is known. It is a machine designed to drive a contact type probe p to scan the surface of a workpiece w such as an optical element or a metal mold, applying it thereto, in order to determine the current three-dimensional coordinate position of the probe.